The present invention relates to a method for cooling a hot-rolled material having a rolled-material cross section, in particular a metal strip, e.g. a steel strip, in a cooling line, comprising the following steps:                a starting temperature is recorded for a rolled-material location upstream of the cooling line,        a temporal quantitative coolant profile is determined on the basis of a cooling-line model and predetermined desired properties of the rolled material,        a coolant is applied to the rolled-material location in accordance with the temporal quantitative coolant profile which has been determined, and        an expected temporal temperature profile of the rolled material at the rolled-material location across the rolled-material cross section is determined on the basis of the cooling-line model and the temporal quantitative coolant profile.        
The present invention also relates to a corresponding cooling-line model.
A cooling method of this type and the corresponding cooling-line model are known, for example, from “Stahl und Eisen”, Volume 116 (1996), No. 11, pages 115 to 120.
The exact modeling of the temporal temperature profile during cooling of a hot-rolled metal strip is of crucial importance for controlling the quantitative coolant profile. Since, furthermore, the cooling is not in thermodynamic equilibrium, phase transitions in the rolled material to be cooled, e.g. a phase transformation in steel, have a crucial effect on the thermal characteristics during cooling. Therefore, the phase transformation has to be incorporated in Fourier's law of heat conduction.
The modeling of the phase transformation in turn requires the temperature as an input parameter. This results in a coupled differential equation system which can be approximately solved numerically, e.g. by a starting value problem solver. In this approach, it is necessary to solve Fourier's heat conduction equation together with the dynamics of the phase transformation.
Two methods are customary in the prior art.
In the first of these, the phase transformation is initially modeled on the basis of an approximate temperature profile. Then, the phase transformation is frozen. The exothermic events in the phase transformation are then taken into account in Fourier's heat conduction equation by means of heat sources. This approach partially neglects the link between the phase transformation and the temperature.
Although another method does couple the phase transformation to the solution to the Fourier's heat conduction equation, in this method too exothermic events in the phase transformation are simulated by heat sources in the Fourier's heat conduction equation.
However, the methods of the prior art only appear to solve the problem. In fact, in both cases the approach is incorrect under the laws of physics. This is demonstrated in particular by the fact that the heat source has to be separately parameterized in the cooling-line model.